Solve {c}{12/4+25/5-12/10}{97/10-5frac{1}{4}-3frac{3}{8}}

$$\left. \begin{array} { c } { 1 \frac { 2 } { 4 } + 2 \frac { 5 } { 5 } - 1 \frac { 2 } { 10 } } \\ { 9 \frac { 7 } { 10 } - 5 \frac { 1 } { 4 } - 3 \frac { 3 } { 8 } } \end{array} \right.$$

Sort

$$\frac{43}{40},\frac{33}{10}$$

Solution Steps

Multiply 1 and 4 to get 4.

$$sort(\frac{4+2}{4}+\frac{2\times 5+5}{5}-\frac{1\times 10+2}{10},\frac{9\times 10+7}{10}-\frac{5\times 4+1}{4}-\frac{3\times 8+3}{8})$$

Add 4 and 2 to get 6.

$$sort(\frac{6}{4}+\frac{2\times 5+5}{5}-\frac{1\times 10+2}{10},\frac{9\times 10+7}{10}-\frac{5\times 4+1}{4}-\frac{3\times 8+3}{8})$$

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

$$sort(\frac{3}{2}+\frac{2\times 5+5}{5}-\frac{1\times 10+2}{10},\frac{9\times 10+7}{10}-\frac{5\times 4+1}{4}-\frac{3\times 8+3}{8})$$

Multiply 2 and 5 to get 10.

$$sort(\frac{3}{2}+\frac{10+5}{5}-\frac{1\times 10+2}{10},\frac{9\times 10+7}{10}-\frac{5\times 4+1}{4}-\frac{3\times 8+3}{8})$$

Add 10 and 5 to get 15.

$$sort(\frac{3}{2}+\frac{15}{5}-\frac{1\times 10+2}{10},\frac{9\times 10+7}{10}-\frac{5\times 4+1}{4}-\frac{3\times 8+3}{8})$$

Divide 15 by 5 to get 3.

$$sort(\frac{3}{2}+3-\frac{1\times 10+2}{10},\frac{9\times 10+7}{10}-\frac{5\times 4+1}{4}-\frac{3\times 8+3}{8})$$

Convert 3 to fraction \frac{6}{2}.

$$sort(\frac{3}{2}+\frac{6}{2}-\frac{1\times 10+2}{10},\frac{9\times 10+7}{10}-\frac{5\times 4+1}{4}-\frac{3\times 8+3}{8})$$

Since \frac{3}{2} and \frac{6}{2} have the same denominator, add them by adding their numerators.

$$sort(\frac{3+6}{2}-\frac{1\times 10+2}{10},\frac{9\times 10+7}{10}-\frac{5\times 4+1}{4}-\frac{3\times 8+3}{8})$$

Add 3 and 6 to get 9.

$$sort(\frac{9}{2}-\frac{1\times 10+2}{10},\frac{9\times 10+7}{10}-\frac{5\times 4+1}{4}-\frac{3\times 8+3}{8})$$

Multiply 1 and 10 to get 10.

$$sort(\frac{9}{2}-\frac{10+2}{10},\frac{9\times 10+7}{10}-\frac{5\times 4+1}{4}-\frac{3\times 8+3}{8})$$

Add 10 and 2 to get 12.

$$sort(\frac{9}{2}-\frac{12}{10},\frac{9\times 10+7}{10}-\frac{5\times 4+1}{4}-\frac{3\times 8+3}{8})$$

Reduce the fraction \frac{12}{10} to lowest terms by extracting and canceling out 2.

$$sort(\frac{9}{2}-\frac{6}{5},\frac{9\times 10+7}{10}-\frac{5\times 4+1}{4}-\frac{3\times 8+3}{8})$$

Least common multiple of 2 and 5 is 10. Convert \frac{9}{2} and \frac{6}{5} to fractions with denominator 10.

$$sort(\frac{45}{10}-\frac{12}{10},\frac{9\times 10+7}{10}-\frac{5\times 4+1}{4}-\frac{3\times 8+3}{8})$$

Since \frac{45}{10} and \frac{12}{10} have the same denominator, subtract them by subtracting their numerators.

$$sort(\frac{45-12}{10},\frac{9\times 10+7}{10}-\frac{5\times 4+1}{4}-\frac{3\times 8+3}{8})$$

Subtract 12 from 45 to get 33.

$$sort(\frac{33}{10},\frac{9\times 10+7}{10}-\frac{5\times 4+1}{4}-\frac{3\times 8+3}{8})$$

Multiply 9 and 10 to get 90.

$$sort(\frac{33}{10},\frac{90+7}{10}-\frac{5\times 4+1}{4}-\frac{3\times 8+3}{8})$$

Add 90 and 7 to get 97.

$$sort(\frac{33}{10},\frac{97}{10}-\frac{5\times 4+1}{4}-\frac{3\times 8+3}{8})$$

Multiply 5 and 4 to get 20.

$$sort(\frac{33}{10},\frac{97}{10}-\frac{20+1}{4}-\frac{3\times 8+3}{8})$$

Add 20 and 1 to get 21.

$$sort(\frac{33}{10},\frac{97}{10}-\frac{21}{4}-\frac{3\times 8+3}{8})$$

Least common multiple of 10 and 4 is 20. Convert \frac{97}{10} and \frac{21}{4} to fractions with denominator 20.

$$sort(\frac{33}{10},\frac{194}{20}-\frac{105}{20}-\frac{3\times 8+3}{8})$$

Since \frac{194}{20} and \frac{105}{20} have the same denominator, subtract them by subtracting their numerators.

$$sort(\frac{33}{10},\frac{194-105}{20}-\frac{3\times 8+3}{8})$$

Subtract 105 from 194 to get 89.

$$sort(\frac{33}{10},\frac{89}{20}-\frac{3\times 8+3}{8})$$

Multiply 3 and 8 to get 24.

$$sort(\frac{33}{10},\frac{89}{20}-\frac{24+3}{8})$$

Add 24 and 3 to get 27.

$$sort(\frac{33}{10},\frac{89}{20}-\frac{27}{8})$$

Least common multiple of 20 and 8 is 40. Convert \frac{89}{20} and \frac{27}{8} to fractions with denominator 40.

$$sort(\frac{33}{10},\frac{178}{40}-\frac{135}{40})$$

Since \frac{178}{40} and \frac{135}{40} have the same denominator, subtract them by subtracting their numerators.

$$sort(\frac{33}{10},\frac{178-135}{40})$$

Subtract 135 from 178 to get 43.

$$sort(\frac{33}{10},\frac{43}{40})$$

Least common denominator of the numbers in the list \frac{33}{10},\frac{43}{40} is 40. Convert numbers in the list to fractions with denominator 40.

$$\frac{132}{40},\frac{43}{40}$$

To sort the list, start from a single element \frac{132}{40}.

$$\frac{132}{40}$$

Insert \frac{43}{40} to the appropriate location in the new list.

$$\frac{43}{40},\frac{132}{40}$$

Replace the obtained fractions with the initial values.

$$\frac{43}{40},\frac{33}{10}$$

Evaluate

$$\frac{33}{10},\ \frac{43}{40}$$